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11111nata11111 [884]
3 years ago
6

Two number cubes (6 sided) are rolled at the same time. What is the probability that the first number cube will land on a 2 or 3

and the second number cube will land on an even number?
Mathematics
1 answer:
Reil [10]3 years ago
7 0

Answer:

5/36 or approximately 13.88...%

Step-by-step explanation:

First, we need to know the probability of rolling a 2 or 3. Because there are 6  sides, the probability is 2/6

Next, we have to find the probability of rolling an even number. With the numbers:

1, 2, 3, 4, 5, 6

1, 3, 5 are odd       2, 4, 6 are even

so, the probability of rolling an even number is 3/6

Finally, multiply the probabilities:

3/6*2/6=5/36

Answer:

5/36 or about 13.88%

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8 0
3 years ago
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Write the first five digits of 1/7 in base 9 expression
kaheart [24]

Compare 1/7 to consecutive multiples of 1/9. This is easily done by converting the fractions to a common denominator of LCM(7, 9) = 63:

1/9 = 7/63

2/9 = 14/63

while

1/7 = 9/63

Then 1/7 falls between 1/9 and 2/9, so 1/7 = 1/9 plus some remainder. In particular,

1/7 = 1/9¹ + 2/63.

We do the same sort of comparison with the remainder 2/63 and multiples of 1/9² = 1/81. We have LCM(63, 9²) = 567, and

1/9² = 7/567

2/9² = 14/567

3/9² = 21/567

while

2/63 = 18/567

Then

2/63 = 2/9² + 4/567

so

1/7 = 1/9¹ + 2/9² + 4/567

Compare 4/567 with multiples of 1/9³ = 1/729. LCM(567, 9³) = 5103, and

1/9³ = 7/5103

2/9³ = 14/5103

3/9³ = 21/5103

4/9³ = 28/5103

5/9³ = 35/5103

6/9³ = 42/5103

while

4/567 = 36/5103

so that

4/567 = 5/9³ + 1/5103

and so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/5103

Next, LCM(5103, 9⁴) = 45927, and

1/9⁴ = 7/45927

2/9⁴ = 14/45927

while

1/5103 = 9/45927

Then

1/5103 = 1/9⁴ + 2/45927

so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/45927

One last time: LCM(45927, 9⁵) = 413343, and

1/9⁵ = 7/413343

2/9⁵ = 14/413343

3/9⁵ = 21/413343

while

2/45927 = 18/413343

Then

2/45927 = 2/9⁵ + remainder

so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/9⁵ + remainder

Then the base 9 expansion of 1/7 is

0.12512..._9

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Which property justifies the following steps:
ad-work [718]
Step 3:
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3 years ago
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Answer:

1

4

9

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64

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49 = 7 x 7 = 7²

64 = 8 x 8 = 8²

81 = 9 x 9 = 9²

100 = 10 x 10 = 10²

4 0
3 years ago
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